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To solve for the present value of a future amount with compound interest, we can use the present value formula for compound interest:

\[
PV = \frac{FV}{(1 + \frac{r}{n})^{n \cdot t}}
\]

where:
- $ PV $ is the present value,
- $ FV $ is the future value (in this case, $14,000),
- $ r $ is the annual interest rate (3%, or 0.03 as a decimal),
- $ n $ is the number of compounding periods per year (quarterly compounding, so $ n = 4 $),
- $ t $ is the number of years (5.5 years).

### Step-by-Step Calculation:

1. **Identify all values**:
   - $ FV = 14000 $
   - $ r = 0.03 $
   - $ n = 4 $
   - $ t = 5.5 $

2. **Plug into the formula**:
   \[
   PV = \frac{14000}{\left(1 + \frac{0.03}{4}\right)^{4 \cdot 5.5}}
   \]

3. **Calculate the quarterly rate**:
   \[
   1 + \frac{0.03}{4} = 1 + 0.0075 = 1.0075
   \]

4. **Calculate the exponent**:
   \[
   4 \cdot 5.5 = 22
   \]

5. **Evaluate the expression**:
   \[
   PV = \frac{14000}{(1.0075)^{22}}
   \]

6. **Final Calculation**:
   \[
   PV \approx \frac{14000}{1.173561} \approx 11926.52
   \]

So, the present value is approximately **$11,926.52**.

Would you like a deeper explanation on any part of this calculation? 

### Related Questions:
1. How does the frequency of compounding affect the present value?
2. What if the interest rate were compounded monthly instead of quarterly?
3. How would the present value change if the future value were $20,000?
4. Can we calculate future values with the same formula?
5. How would an increase in the interest rate to 4% affect the present value?

### Tip:
Always double-check the frequency of compounding in financial calculations, as it can significantly impact the results.

Find the present value for the following future amount: $14,000 at 3% compounded quarterly for 5.5 years.

Learn how to find the present value of $14,000 with 3% interest compounded quarterly over 5.5 years. This solution uses the compound interest formula to calculate the initial amount required for a given future value. Suitable for advanced high school or college-level students.

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